MIMO Systems Theory and Applications Part 2 ppt

Combining techniques for MIMO systems MIMO system can use several techniques at the receiver so that to combine the multipleincoming signals for more robust reception.. The received sign

0 5 10 15 20 0

5 10 15 20 25

SNR (dB)

Uniform power allocation Optimal power allocation Optimal power allocation (Uncorrelated MIMO channel)

Fig 12 MIMO(4×4): Capacity improvement with WF strategy-Channel correlation impact

on system capacity

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Capacity(bits/s/Hz)

NoWF−SNR=6dB NoWF−SNR=10dB WF−SNR=6dB WF−SNR=10dB

SNR=6dB

SNR=10dB

Fig 13 CCDF for MIMO(4×4)with various SNR values

0 5 10 15 20 2

4 6 8 10 12 14

SNR (dB)

No WF WF

Fig 14 Ergodic capacity for MIMO(4×2)-Kronecker channel model

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Capacity (bits/s/Hz)

NoWF WF

Fig 15 CCDF for MIMO(4×2)-Kronecker channel model (SNR=18dB)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Capacity (bits/s/Hz)

NoWF WF

Fig 16 CCDF for MIMO(4×2)-Kronecker channel model (SNR=2dB)

6 Combining techniques for MIMO systems

MIMO system can use several techniques at the receiver so that to combine the multipleincoming signals for more robust reception Combining techniques are listed below :

1 Maximal Ratio Combining (MRC): Incoming signals are combined proportional to the SNR

of that path signal The MRC coefficients correspond to the relative amplitudes of the pulsereplicas received by each antenna such that more emphasis is placed on stronger multipathcomponents and less on weaker ones

2 Equal Gain Combining (EGC) simply adds the path signals after they have been cophased(Sanayei & Nosratinia, 2004)

3 Selection Combining (SC) selects the highest strength of incoming signals from one of thereceiving antennas

Combining techniques can be carried so that to satisfy one or more targets :

1 Maximizing the diversity gain

2 Maximizing the multiplexing gain

3 Achieving a compromise between diversity gain and multiplexing gain

4 Achieving best performances in terms of Bit Error Rate (BER)

5 Maximizing the Frobenius norm of the MIMO channel and therefore the MIMO channelcapacity

Let us recall the SIMO system model with N R receive antennas The received signal at the q-th

receive antenna is expressed as :

• P T: Transmit signal power

• γ= P T

σ2

b

is the SNR

We assume channel normalization and a perfect channel estimation We will be more

interested in the combining module Our aim is to derive the combining coefficients gq ; q=

1, , N R The output signal at the combining module can be expressed as:

Combining technique in MIMO system is depicted in Fig.17 Combining coefficients relative

to the listed techniques are given by:

Combining technique Combining coefficient

~-

Fig 17 SIMO system with combining technique

6.1 Maximal Ratio Combining (MRC)

The equivalent SNR of MRC has been calculated as :

The system capacity with MRC is :

6.2 Equal Gain Combining (EGC)

The instantaneous SNR is expressed as :

of the receiver is directly resolvable paths (Zhou & Okamoto, 2004) In general, EGC performsworse than does MRC Obviously, lower capacity is obtained with SC since only one RadioFrequency (RF) channel is selected at the receiver A study of combining techniques interms of BER was presented in (Zhou & Okamoto, 2004) MRC steel achieves the best BERperformances

7 Beamforming processing in MIMO systems

Beamforming is the process of trying to steer the digital baseband signals to one particulardirection by weighting these signals differently This is named "digital beamforming" and

we call it beamforming for the sake of brevity, (Jafarkhani, 2005) The desired signal is thenobtained by summing the weighted baseband signals

7.1 Beamforming based on SVD decomposition

In this section, we provide an overview of MIMO systems that use beamforming at both

the ends of the communication link We consider a MIMO system with N T transmit

and N R receive dimensions From a mathematical point of view, joint Transmit-Receivebeamforming is based on the minimization (or maximization) of some cost function such asSNR maximization This method includes determining the transmit beamforming coefficientsand the receive beamforming coefficients so that to steer relatively all transmit energy andreceive energy in the directions of interest Joint Transmit-Receive beamforming is illustrated

• x: The transmit signal

• Wt= [Wt1, .,WtN ]T: The(N T ×1)Transmit beamforming vector

• H: The(N R × N T)channel matrix

• Wr= [Wr1, .,WrN R]T: The(N R ×1)Receive beamforming vector

• b= [b 1 , , b N R]T: The(N R ×1)Additive noise vector with varianceσ2

b

• yBF: The output signal

Joint Transmit-Receive beamforming can be described by equation (70)

yBF=WrHHW t·x+WrH ·b (70)Eigen-beamforming could be performed by using eigenvectors to find the linear beamformerthat optimizes the system performances Thus, we exploit the SVD factorization for channel

matrix H (H = USVH) Assigning U and V respectively to Wr and Wt is optimal for

maximizing the SNR given by :

SNRBF= WrHHWt 2E(xxH)

σ2

b Wr 2When SVD factorization is applied to MIMO channel matrix, equation (70) becomes :

yBF=S·x+UH ·b (71)Note that Beamforming (Ibnkahla, 2009) is considered as a form of linear combiningtechniques which are intended to maximize the spectral efficiency The received SNR forcommunication system with beamforming is expressed as :

• System performing beamforming

• Transmission without applying beamforming

• Transmission with simply Zero Forcing (ZF) equalization

The MIMO(3×3)channel is randomly generated and input signal is BPSK modulated Weadopt the correlated MIMO channel with a spreading angle of 90◦and an antenna spacing of

λ

2 Fig 21 shows that associated SVD beamforming technique brings the best performances interms of BER

0 5 10 15 20 1

2 3 4 5 6 7 8 9 10 11

SNR(dB)

SISO MIMO(2X2) MIMO(3X3) MIMO(4X4)

Fig 20 Capacity of MIMO system with beamforming technique

Fig 21 SVD based beamforming technique

7.2 SINR maximization beamforming

Interference often occurs in wireless propagation environment When several terminals aredensely deployed in the coverage area, Signal to Interference Noise Ratio (SINR) grows upand efficient techniques are required to be implemented Beamforming is an efficient strategythat could be exploited so that to mitigate interference Maximizing the SINR criteria could bealso considered so that to obtain optimal beamforming weights

SINR maximization based beamforming in Multi user system

• E= [e1, , eN]T: The transmit signal vector

• Wt=[Wt1, .,WtK]T: Weight vector for beamforming

• M1, , MK number of antennas respectively for users U1, , UK

• x: The transmit vector signal of size(N ×1)

Transmit signal is expressed as :

biis the additive noise with varianceσ2

i The channel matrix Hi(M i × N)between user U iwith

M i antennas and the N antennas at the Base Station (BS) is assumed to be normalized User

U i ; i=1, , K receives the signal :

The SINR is the ratio of the received strength of the desired signal to the received strength of

undesired signals (Noise + Interference) Associated SINR to user i is expressed as :

Fig 23 Multi user BF (K=3, M=3/M=4)

8 Processing techniques for MIMO systems: Antenna selection

MIMO system gives high performances in terms of system capacity and reliability ofradio communication Combining techniques such as MRC results in more robust system.Nevertheless, the deployment of multiple antennas would require the implementation ofmultiple RF chains (Dong et al., 2008) This would be costly in terms of size, power andhardware For example, when several antennas are deployed, multiple RF chains withseparate modulator and demodulator have to be implemented To overcome these limitations,antenna selection techniques can be applied

8.1 Antenna selection

Antenna selection technique (Ben ZID et al., 2011) is depicted in Fig 24 We consider a MIMO

system with N T transmit antennas and N Rreceive antennas The idea of antenna selection is

to select L T antennas among the N T transmit antennas and / or L R antennas among the N R

receive antennas We distinguish different forms of antenna selection:

1 Transmit antenna selection

2 Receive antenna selection

3 Hybrid antenna selection: that is when antenna selection is carried among both transmitantennas and receive antennas

Fig 24 Antenna selection in MIMO system

Antenna selection algorithms do not only aim to reduce the system complexity but also to

achieve high spectral efficiency When L T antennas are selected at the transmitter and L R

antennas are selected at the receiver, the associated channel will be denoted HS The capacity

of such system is expressed as :

CSel=log2

det I L T+ γ

γ denotes the SNR The antenna selection algorithm is intended to find the optimal subset

of the transmit antennas and /or the optimal subset of the receive antennas that satisfycapacity system maximization Nevertheless, it is obvious that the joint antenna selection

at the transmitter and the receiver brings more complexity when the number of antennasincreases

Numerical results

Ergodic capacity of MIMO system with antenna selection at the transmitter and the receiver

is shown in Fig 25 For simulation purposes, we generate a Rayleigh MIMO channel withAWGN Here, SVD factorization is applied Plotted curves depict the ergodic capacity for theMIMO(4×4) This evidently leads to the highest system capacity When 3 transmit antennasare selected among 4 transmit antennas and 3 receive antennas are selected among 4 receiveantennas, the maximum ergodic capacity that could be achieved is plotted in function of SNR.Simulation results are also presented in the case when two antennas are selected at both thetransmitter and the receiver According to the plotted curves in Fig 25, it is obvious that one ofthe important limitations of the antenna selection strategy is the important losses in capacity

at high SNR regime

5 10 15 20 25 30 35

8.2 Antenna selection involving ST coding

We present in this paragraph, the simulation results in terms of average BER when jointAlamouti scheme and antenna selection at the receiver are applied The MIMO(4×2)systemwith a Rayleigh channel and AWGN was created Emitted symbols are QAM (Quadrature

Amplitude Modulation) modulated The simulation model is given by the Fig 26 (b1, , b N R

denote the additive noise signals) Plotted curves concern subsets of receive antennas where

L R=1 and LR=3 Simulation results show that even with only one selected antenna at the

-L R

STdecoder

Alamouti

encoder

Antennaselection

R =3 L

R =4

Fig 27 Joint Alamouti coding and antenna selection in MIMO(4×2)

receiver, performances in terms of BER still satisfactory Nevertheless, when more antennasare selected, better BER values are achieved thanks to receive diversity

Tx Rx

yx

y

yz

j:ΔR

Scatterers

R

*



Fig 28 Angle spread

8.3 Antenna selection in correlated MIMO channel: Angular dispersion and channel

correlation

Angle spread refers to the spread of DOA of the multipath components at the transmit antennaarray When scatterers are also distributed around the receive antennas, the scattering effectleads also to an angle spreading relative to the DOA In Fig 28, the angle spread is denotedΔR

We present a SISO model rich of local scatterers For seek of simplicity, we consider a MIMO(N R × N T)system with LOS channel and uniform antenna arrays at both the transmitter andthe receiver

We denote :

• H: MIMO channel matrix

• dq,p: distance between antenna q and antenna p

• ρ q,q : correlation coefficient

• λ: wavelength

• R=E[HHH]Correlation matrix

• α: Angle of arrival

• p(α): Probability density function of the DOA

• ΔR(=2π): Angle spread at the receiving side

When LOS propagation is assumed, the channel coefficients can be expressed as :

h qp=e −j2π dq,p λ ; q=1, , NR, p=1, , NT (82)The correlation coefficient at the receiving side between two receive antennas of indexes q and

q is expressed :

ρ q,q  =E[exp (− j2π d q,q  λ sinα)] (83)Formula for correlation coefficients is expressed as :

Following a uniform distribution, correlation coefficients can be expressed as :

to simulation results depicted in Fig 29, we conclude that spatial correlation between twoantennas depends on antenna spacing and is reduced by higher angle spread

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fig 29 Impact of angle spread on spatial correlation

Better performances in terms of BER are achieved for AS=30◦ This is due to the fact that for

a given antenna spacing, system correlation is higher for lower angular spread The impact ofangle spread on system performances is depicted in Fig 30

9 Multi polarization techniques

9.1 Basic antenna theory and concepts

We present in this paragraph, some basic concepts related to antenna A rigorous analysis ofthe antenna theory and the related concepts is available in (Constantine, 2005) Antenna is atransducer for radiating or receiving radio waves It ideally radiates all the power delivered

to it from the transmitter in a desired direction The far electric field of the electromagneticwave is written in spherical coordinates as :

E=E θ(θ, φ)ˆθ+E φ(θ, φ)φˆ (87)

Fig 30 Impact of angle spread on system performances

E θ and E φare the electric field components.θ and φ denote respectively the elevation angle

and the azimuthal angle We distinguish two categories of antennas :

1 Omnidirectional antenna is an antenna system which radiates power uniformly

2 Dipole antenna radiates power in a particular direction

Electric dipole could be oriented along the x-axis, y-axis or the z-axis Table 2 gives theexpressions of the electric field components relative to each antenna orientation

E θ(θ, φ) E φ(θ, φ)

x−cos(θ)cos(φ) sin(φ)

y−cos(θ)sin(φ ) −cos(φ)

z sin(θ) 0Table 2 Radiation pattern for electric dipole

π

0

|E θ(θ, φ ) |2dΩ+

2π

0

π

0

π

0

|E θ(θ, φ ) |2dΩ+

2π

0

π

0

• Ω is the beam solid angle through which all the power of the antenna would flow if itsradiation intensity is constant for all angles withinΩ.

• G θ(θ, φ) and G φ(θ, φ) are respectively the elevation antenna gain and the azimuthalantenna gain

9.2 3D Geometric wide band channel model

The 3D Geometric wide band channel model is presented in Fig.31

R x

T x

v

vv

vu

u

u

uu

uv

v

vv

ww

w

ww



?

θ ( ,n) Rx

- y



-Fig 31 3D Geometric model for MIMO channel (N R=2, N T=2)

Two transmit antennas (ATx(1),A(2)Tx) and two receive antennas (A(1)Rx,A(2)Rx) are presented Wideband MIMO channel involves several local clusters of scatterers which are distributed aroundthe transmitter and the receiver The cluster index is denoted,  = 1, , L Cluster around the transmitter CTx() is assumed to be associated with a set of M ()scatterers(STx(,m); m=

1, , M ()) Cluster around the receiver CRx() is assumed to be associated with a set of N ()

scatterers(S (,n)Rx ; n=1, , N ())

We take for notations:

• RTx(): Transmit cluster radius of index

• D()Tx: Distance between the reference transmit antenna and the transmit cluster center

• d1,,m : Distance between antenna A(1)Tx and a scatterer S (,m)Tx

• d2,,m : Distance between antenna A(2)Tx and a scatterer S (,m)Tx

• dTx: Transmit antennas spacing

• DTx↔Rx: Distance between the transmitter and the receiver

• RRx(): Cluster radius at the receiver of index